[brandmeyer]

The error in logic is the part where you see so much empty space for wind to pass through. The horizontal velocity of the wind is quite a bit lower than the circumferential velocity of the turbine blade. So only a relatively short distance passes before another blade comes along.

I had a great animation in mind that shows it clearly, but I can't seem to find it right now. To get a static idea, See the corkscrew graphics in figures 4.18 and 4.19 of https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1...

Basically, there is a relationship between number of blades, blade tip speed, and flow speed that is optimized. For the same flow speed, power, and area, a two-blade turbine has to spin faster to reach optimum and makes more drag. A four-blade turbine has to spin slower to reach optimum, but it is only barely closer to the Betz limit than the corresponding optimized three-blade turbine. The difference is small enough that its difficult to measure or simulate - some other inter-blade losses rise in importance as well.

edit to add: Here's a deep dive into tip speed ratio as it applies to wind turbine design: https://cdn.intechopen.com/pdfs/16242/InTechWind_turbines_th...